Generating functions for symmetric and shifted symmetric functions

TL;DR

This paper presents a unified approach using vertex operators to generate and analyze classical symmetric functions and their shifted counterparts, enhancing understanding of their structure and relationships.

Contribution

It introduces a vertex operator-based method to generate and study symmetric and shifted symmetric functions in a unified framework.

Findings

Unified generating functions for symmetric and shifted symmetric functions

Vertex operator realization as a versatile tool

Simplified derivation of classical and shifted symmetric functions

Abstract

We describe generating functions for several important families of classical symmetric functions and shifted Schur functions. The approach is originated from vertex operator realization of symmetric functions and offers a unified method to treat various families of symmetric functions and their shifted analogues.